Frequency Calculator

Calculate frequency, period, or wavelength. Enter period OR wavelength with wave speed to find frequency.

Frequency Formulas: 1. From Period: f = 1/T 2. From Wavelength: f = v/λ Where: • f = frequency (hertz, Hz) • T = period (seconds, s) • v = wave speed (m/s) - Sound in air: ~343 m/s (20°C) - Light in vacuum: 299,792,458 m/s • λ = wavelength (meters, m) Rearrangements: • Period: T = 1/f • Wavelength: λ = v/f Angular frequency: ω = 2πf (rad/s)
Example 1 (From period): A pendulum has period T = 2 s f = 1/2 = 0.5 Hz (one swing every 2 seconds) Example 2 (From wavelength - sound): Sound wave λ = 0.5 m in air (v = 343 m/s) f = 343/0.5 = 686 Hz (musical note F5) Example 3 (From wavelength - light): Red light λ = 700 nm = 700×10⁻⁹ m f = (3×10⁸)/(700×10⁻⁹) = 4.29×10¹⁴ Hz = 429 THz Example 4 (Period from frequency): AC power at 60 Hz T = 1/60 ≈ 0.0167 s = 16.7 ms per cycle Example 5 (Wavelength from frequency): FM radio at 100 MHz = 100×10⁶ Hz λ = (3×10⁸)/(100×10⁶) = 3 m Example 6 (Musical note): Middle C = 261.63 Hz T = 1/261.63 ≈ 0.00382 s = 3.82 ms Sound wavelength: λ = 343/261.63 ≈ 1.31 m

What is frequency?

Frequency is the number of complete cycles or oscillations per unit time, measured in hertz (Hz). 1 Hz = 1 cycle/second. For example, a 60 Hz power line completes 60 cycles each second.

What is the relationship between frequency and period?

Frequency and period are reciprocals: f = 1/T and T = 1/f. Period (T) is the time for one complete cycle. If a wave has period 0.02 s, its frequency is 1/0.02 = 50 Hz.

How do you calculate frequency from wavelength and wave speed?

Use f = v/λ, where v is wave speed and λ is wavelength. For example, light with wavelength 500 nm travels at c = 3×10⁸ m/s, so f = (3×10⁸)/(500×10⁻⁹) = 6×10¹⁴ Hz.

What are common frequency units?

Hz (hertz) = 1 cycle/s; kHz (kilohertz) = 1,000 Hz; MHz (megahertz) = 10⁶ Hz; GHz (gigahertz) = 10⁹ Hz; THz (terahertz) = 10¹² Hz. Radio: kHz-GHz; visible light: ~400-800 THz.

What is angular frequency and how does it relate to frequency?

Angular frequency ω (omega) is in radians/second: ω = 2πf. It's used in wave equations and circular motion. For f = 60 Hz, ω = 2π(60) ≈ 377 rad/s. Regular frequency counts cycles; angular frequency counts radians.

Can frequency be negative?

No, frequency is always positive or zero as it counts oscillations per time. However, in complex signal analysis, "negative frequencies" represent phase information (they're mathematical constructs, not physical negative cycles).

What is the frequency range of human hearing?

Humans typically hear 20 Hz to 20,000 Hz (20 kHz). Below 20 Hz is infrasound (felt more than heard); above 20 kHz is ultrasound. Age reduces upper limit - many adults lose sensitivity above 15 kHz.

How does frequency affect wave energy?

For electromagnetic waves, energy E = hf (Planck's equation), where h = 6.626×10⁻³⁴ J·s. Higher frequency means higher energy per photon. This is why UV (high f) causes sunburn but radio waves (low f) don't.

What are real-world applications of frequency?

Radio/TV broadcasting (kHz-GHz), musical notes (A4 = 440 Hz), electrical grids (50/60 Hz), WiFi (2.4/5 GHz), medical ultrasound (1-20 MHz), atomic clocks (GHz), and color (light frequency determines color).

What is the Doppler effect on frequency?

Moving sources/observers shift frequency. Approaching: higher frequency (blue shift); receding: lower frequency (red shift). Formula: f' = f(v±v_o)/(v∓v_s), where v is wave speed, v_o observer speed, v_s source speed.

How do you measure frequency?

Instruments include: frequency counters (count cycles/time), oscilloscopes (measure period visually), spectrum analyzers (show frequency content), and FFT (Fast Fourier Transform) algorithms that convert time-domain signals to frequency-domain.

What is resonance frequency?

Resonance is when a system oscillates at maximum amplitude, occurring at its natural frequency. Examples: tuning fork, radio tuning, bridge collapse (Tacoma Narrows), breaking glass with voice. Formula varies: spring-mass f = (1/2π)√(k/m).